and the shape of the conic section depend on the initial parameters of the planet's trajectory. One may vary the

00:27

absolute value of the initial velocity keeping its direction and the solar distance constant. Here,

00:43

the sun is in the left focus of a small ellipse. A certain velocity results

00:55

in a circular orbit. These

01:05

examples show that, even if all motions follow from one differential equation, each single trajectory is dependent on the initial

01:18

position and initial velocity of

01:21

the planet. Scale variation 1:2 Here, a somewhat elongated ellipse develops with the sun in the focus on the right. It can clearly be seen

01:36

that the planet moves faster near-the sun than far from

01:42

it. Starting with still higher

01:45

velocity the planet eventually leaves the solar system on a hyperbolic trajectory, here compared to

01:56

an ellipse. Again, the starting direction makes a right angle

02:02

with the line connecting sun and planet. However, this angle

02:09

may be also acute, for instance +60 degrees. In this case a much more elongated

02:17

ellipse results. Here, both can be compared. Obviously the same is true in the other direction, i. e. -60 degrees.

02:29

The absolute value of the velocity is still the same,

02:35

only the directions vary. Again a flat ellipse results. Here compared to the first one. The third parameter to be

02:47

varied is the initial solar distance. In this and the following examples the initial velocity vector is kept constant. In

03:00

the first example the sun is in the right focus. The next orbit is circular. If one starts the trajectory

03:11

at a still greater distance, again an ellipse results, but the sun is now in the left focus. Increasing the initial distance further eventually results

03:27

in a hyperbolic trajectory. Kepler's second law: The angular momentum

03:35

with respect to the sun is constant. This means that the position vector of a planet relative to the sun sweeps out equal areas of the ellipse in equal times. These areas are shown here. momentum of the planet with respect to the sun is A modern physicist generally formulates constant. This follows from the existence of a central force this law differently: The angular between sun and planet. Kepler's

04:06

third law tells us something about the periods of planetary revolution: The squares of the

04:15

periods of revolution are proportional to the cubes of the semimajor axes of planetary orbits. Here, the ratio of the two periods is two. For the ratio of the semimajor axes one gets two to the two-thirds power or cubic root of two squared. The planets are moving with corresponding velocities. To make the situation clearer in the picture they are stopped after each revolution.

Technische Metadaten

Inhaltliche Metadaten

The film demonstrates Kepler's three laws of planetary motion. In addition the first part shows that a trajectory is determined not only by the forcefield but also by the initial condition of the motion.